The opening first half produced few chances, but Cherries striker Matt Tubbs squandered a rare opportunity when one-on-one with Dons goalkeeper David Martin by firing wide.
MK Dons punished Bournemouth on the 32nd minute through defender Doumbe, who was left unmarked in the penalty area and reacted quickest to fire home a loose ball from Dean Bowditch’s in-swinging corner.
Bournemouth’s problems could have worsened after the interval when a frustrated Donal McDermott lunged with both feet at Bowditch, but escaped with just a booking from referee Darren Deadman.
The visitors should have secured all three points in the 52nd minute when Charlie MacDonald waltzed through the Cherries defence and crashed a shot against the crossbar.
Bournemouth rarely threatened after that, leaving Karl Robinson’s side to record a comfortable third successive league win.